Normally people who like various degrees of pain or something other than typical soft caresses will do this for sexual gratification. This is also the same thing as tit torture (aka titty torture, breast torture and tittie torture)
It may involve breast bondage with ropes and such, nipple clamps, slapping or whipping the breasts, temporary or play piercing with *sterile* piercings, low temperature melted wax, ice cubes, biting and pinching, suction with something other than a person's mouth, electricity with devices meant only for use on the human body, chemical play with substances such as peppermint oil and menthol, and abrasion (sand if you're on the beach, rough fabric, or other textured items).

I got totally nude from the waist up for nipple torture, set the camera on continuous shot so I could have pictures for later, and began to prepare my nipples by setting the air conditioner on high (you know how the refrigerated foods section does at the store, lol). My nipples got so cold and tight, and totally ready.
I started out by capturing my nipple buds between two incredibly heavy books and it hurt so good. It looked amazing from the mirror, and my pussy began to get wet. After another minute, I needed them out, so I sloooowly pulled back. They were *really* caught, so I gave them a hard yank and they popped out with a bounce. Then I took two bottles of lotion without the lids, and I suctioned one to each nipple. I could see inside, and my nipples started to bulge and get red. I knew they would probably now be super-sensitive, so I moved the bottles back and forth so that my nipple buds appeared and disappeared in and out of them quickly.
I tugged on the bottles and they popped off my nipples with a loud slurp. My nipples were now covered in lotion. As I rubbed it in, I pinched and tugged on my nipples with my fingers.
I continued nipple torture by taking a rough washcloth and rubbing vigorously at my nipples, and they hardened even more. I wanted to test how hard they could get, so I put ice cubes...